The border region between Turkey and Iraq is the source of much tension
Iraqi President Jalal Talabani has told Kurdish guerrillas using northern Iraq as a base for attacks on Turkey to lay down their arms or leave the territory.
He was speaking alongside his Turkish counterpart, Abdullah Gul, who is the first Turkish head of state to visit Iraq for more than 30 years.
Relations were sharply tested last year when Turkish forces crossed into Iraq in pursuit of PKK Kurdish rebels.
The Kurdistan Workers' Party (PKK) wants more autonomy in parts of Turkey.
Last year, Ankara accused Iraq of failing to stop the group's attacks.
While Iraq promised to step up co-operation with Turkey against the PKK, Mr Talabani, himself a Kurd, appealed for more cultural freedoms for Turkey's 12 million Kurds.
Although this is the first visit to Iraq by a Turkish head of state in 33 years, it is the third time the two presidents have met this month.
Turkish President Abdullah Gul is seeking closer ties with Iraq
The visit is being seen in Turkey as an attempt to shore-up relations with its neighbour as US troops prepare to withdraw, the BBC's Sarah Rainsford in Istanbul says.
And it comes amid talk of a possibly ground-breaking development, she adds.
Mr Talabani has said a major conference of Kurdish groups from around the world will soon be held in northern Iraq.
And it will be at this summit that Kurds, for the first time, will call on the PKK to end its struggle against Turkey, our correspondent says.
Turkish analysts believe Iraq's Kurds have made a careful calculation, our correspondent adds.
When the US troops leave Iraq, the Kurds will need the support of Turkey on their border to ensure their autonomy - and this will not happen unless they distance themselves from the PKK.
The PKK - which is treated as a terrorist organisation by Turkey, the EU and US - has waged a violent campaign for Kurdish autonomy since 1984, resulting in more than 40,000 deaths.
However, Mr Gul's visit is also about trade between the two countries, which has grown substantially since violence in Iraq declined, the BBC's Hugh Sykes in Baghdad says.
Iraq sells oil to Turkey, while Turkey's exports to northern Iraq include domestic goods, cement and foods amounting to $4bn in 2008.
Turkey's trade minister has said a wealthy Iraq would mean a wealthy Turkey, our correspondent reports.
The two nations will also discuss water. The Tigris and Euphrates rivers originate in Turkey but flow through Iraq, which is concerned that Turkish dams are restricting water supply to the Iraqi people.